@Sean Gimpert, congrats on your purchase!
I can't speak to how HUD goes about it, but if you are asking how the rent is calculated for a section 8 voucher holder, I can provide some insight. The amount listed on the payment standards pd. is the max amount they will pay, but the house has to be inspect and qualified. That is, there needs to be other comparable houses (3 or more) that rent for that amount and the comparables must be within approximately 300 sf. in size to the subject property. That said, if the subject property (the house you are renting) is of higher quality finishes, amenities, etc., and the housing inspector can justify it, it may be approved for a higher rent amount than comps. After that has been established, the utility (gas, water, electricity, etc) allowance comes into play. A pdf. Containing info on these amounts can be found on the Housing Authority Of Joliet website. If the tenant is to pay for some or all of the utilities, and the voucher holder/tenant does not have an income, then the amount gets deducted from the approved rental amount.
Then there is one more thing, and I'm not 100% clear if this is the way it works, so please don't take it as gospel. It's just a general idea of how I understand it to work.
If they do have income then a certain percentage of the income (I believe no more than 30%) is calculated and that amount is the responsibility of the tenant to pay towards rent. Part of their income can also go towards offsetting some or all of the utilities allowance. I also think that, depending on how much they make, the tenant is allowed to pay more than the max approved rent amount- but must be approved by housing authority. IE., If you want $2200 for rent but it is approved for $2000 less utilities allowance of $296, the total rent to landlord is $1904. If tenant has sufficient income, some of it can go towards offsetting utilities allowances and possibly towards additional rent, increasing the total rent to landlord.